Question

screen is separate from double slit source at 2 m the distance between the two slits is 0.05mm the second order bright fringe (m=5)is 8.5cm from the center line .(a) determine the wavelength of the light.(b) calculate the distance between adjaseet bright fringe

Answer 1

Given,

Distance between slits and screen $\ D=2\ m$

Distance between two slits $d=0.05\ mm= 5\times 10^{-5}\ m$

Second order bight fringe is 8.5 cm from center line

(a) We know,

Position of $2^{nd}$ order bright fringe

$$y_2=\dfrac{2\lambda D}{d}\\ \Rightarrow \lambda = \dfrac{y_2\times d}{2D}\\ \ \\ \Rightarrow \lambda = \dfrac{8.5\times 5\times 10^{-7}}{4}=1062.5\ nm$$

(b.) The distance between adjacent bright fringe

$$\Delta y= \dfrac{\lambda D}{d}=\dfrac{1062.5\times 10^{-9}\times2}{5\times 10^{-5}}=42.5\times 10^{-3}\ m=42.5\ mm$$